Abstract
Pyramids—with one quadrilateral and four triangular faces—appear as `glueing' elements in a hybrid mesh consisting of tetrahedral and hexahedral elements. High-order discrete differential forms on tetrahedral and hexahedral elements are well known, but the analogous elements on a pyramid are not. How does one construct high-order approximation spaces on pyramids that are compatible with neighbouring elements? We address this question in this paper. We present a family of high-order finite element approximation spaces on a pyramid and associated unisolvent degrees of freedom. These spaces consist of rational basis functions. We establish conforming, exactness and polynomial approximation properties of these new finite elements.
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